Sarvar Kassaei - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Farhad Hosseinzadeh Lotfi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Alireza Amirteimoori - Department of Applied Mathematics, Islamic Azad University, Rasht, Iran
Mohsen Rostamy-Malkhalifeh - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Bijan Rahmani - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Congestion is one of the important concepts in data envelopment analysis that occurs when excessive inputs reduce the maximally possible outputs. Identification and elimination of congestion have a significant impact on reducing inputs along with increasing outputs. Hence, various studies have been conducted to detect and evaluate congestion. However, in today's world, no organization can achieve its final output with just one process of input. In other words, today's organizations have a network structure that consists of several subsections. Ignoring the existing influences among the subsections processes may lead to inadequate or even incorrect results for evaluating the congestion. While all of the existing methods only evaluate the congestion of each subsection or the whole system independently. Therefore, in this paper, the concept of congestion is developed for a specific and so practical case of network structure called “two-stage network structure”. This case of network structure consists of two series stage such that stage ۱ consume some primary inputs to produce some intermediate outputs. In the following, the intermediate outputs are used as the inputs of stage ۲ to produce the final output. Here, the concept of congestion is defined for systems with a two-stage structure. Then, to examine the congestion of each stage as well as the congestion of the whole system, a single linear programming model is proposed. The validity of the proposed model is investigated using several theorems and it is shown that the new definition is a generalization of the previous definitions of the congestion for the black-box systems. Finally, the proposed model is applied to a case study including ۲۴ non-life insurance companies in Taiwan.

Network Data Envelopment Analysis, Two-stage network structure, Intermediate output, Congestion